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Distribution-free confidence intervals for quantile intervals based on current records

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  • Ahmadi, J.
  • Balakrishnan, N.

Abstract

Suppose we know the combined number of upper and lower records and the current values of the lower and the upper records. Then, it is shown how various exact non-parametric confidence intervals can be constructed based on this information. Such intervals are exact and distribution-free in that the corresponding coverage probabilities are known exactly without any assumption about the parent distribution other than that its distribution function is continuous. Distribution-free outer and inner confidence intervals are obtained for quantile intervals based on current records. An exact expression for the confidence coefficient of these outer and inner confidence intervals are derived. Upper and lower confidence limits for quantile differences are obtained. A data set representing the record values of average July temperatures in Neuenburg, Switzerland, is used to illustrate the results.

Suggested Citation

  • Ahmadi, J. & Balakrishnan, N., 2005. "Distribution-free confidence intervals for quantile intervals based on current records," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 190-202, December.
    • Handle: RePEc:eee:stapro:v:75:y:2005:i:3:p:190-202
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    References listed on IDEAS

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    1. J. Ahmadi & N. Arghami, 2003. "Nonparametric confidence and tolerance intervals from record values data," Statistical Papers, Springer, vol. 44(4), pages 455-468, October.
    2. Olivier Guilbaud, 2001. "Exact Non‐parametric Confidence Intervals for Quantiles with Progressive Type‐II Censoring," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(4), pages 699-713, December.
    3. Olivier Guilbaud, 2004. "Exact Non‐Parametric Confidence, Prediction and Tolerance Intervals with Progressive Type‐II Censoring," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(2), pages 265-281, June.
    4. Ahmadi, J. & Balakrishnan, N., 2004. "Confidence intervals for quantiles in terms of record range," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 395-405, July.
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    Cited by:

    1. Jafar Ahmadi & N. Balakrishnan, 2012. "Outer and inner prediction intervals for order statistics intervals based on current records," Statistical Papers, Springer, vol. 53(3), pages 789-802, August.
    2. Ahmadi, Jafar & Balakrishnan, N., 2009. "Pitman closeness of record values to population quantiles," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2037-2044, October.
    3. Ahmadi, Jafar & Balakrishnan, N., 2010. "Pitman closeness of current records for location-scale families," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1577-1583, November.
    4. Jazaa S. Al-Mutairi & Mohammad Z. Raqab, 2020. "Confidence intervals for quantiles based on samples of random sizes," Statistical Papers, Springer, vol. 61(1), pages 261-277, February.
    5. Morteza Amini & Narayanaswamy Balakrishnan, 2015. "Pooled parametric inference for minimal repair systems," Computational Statistics, Springer, vol. 30(2), pages 605-623, June.
    6. Ahmadi, J. & Razmkhah, M. & Balakrishnan, N., 2009. "Current k-records and their use in distribution-free confidence intervals," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 29-37, January.
    7. Amini, Morteza & Balakrishnan, N., 2013. "Nonparametric meta-analysis of independent samples of records," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 70-81.
    8. Ahmadi, J. & Balakrishnan, N., 2008. "Nonparametric confidence intervals for quantile intervals and quantile differences based on record statistics," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1236-1245, August.
    9. Raqab, Mohammad Z. & Balakrishnan, N., 2008. "Prediction intervals for future records," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1955-1963, September.
    10. Ahmadi, Jafar & MirMostafaee, S.M.T.K. & Balakrishnan, N., 2010. "Nonparametric prediction intervals for future record intervals based on order statistics," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1663-1672, November.

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